This function computes the inverse of the one-dimensional n-point
discrete Fourier Transform of real input computed by rfft.
In other words, irfft(rfft(a),len(a))==a to within numerical
accuracy. (See Notes below for why len(a) is necessary here.)

The input is expected to be in the form returned by rfft, i.e. the
real zero-frequency term followed by the complex positive frequency terms
in order of increasing frequency. Since the discrete Fourier Transform of
real input is Hermitian-symmetric, the negative frequency terms are taken
to be the complex conjugates of the corresponding positive frequency terms.

Parameters:

a : array_like

The input array.

n : int, optional

Length of the transformed axis of the output.
For n output points, n//2+1 input points are necessary. If the
input is longer than this, it is cropped. If it is shorter than this,
it is padded with zeros. If n is not given, it is determined from
the length of the input along the axis specified by axis.

axis : int, optional

Axis over which to compute the inverse FFT. If not given, the last
axis is used.

Returns:

out : ndarray

The truncated or zero-padded input, transformed along the axis
indicated by axis, or the last one if axis is not specified.
The length of the transformed axis is n, or, if n is not given,
2*(m-1) where m is the length of the transformed axis of the
input. To get an odd number of output points, n must be specified.

Returns the real valued n-point inverse discrete Fourier transform
of a, where a contains the non-negative frequency terms of a
Hermitian-symmetric sequence. n is the length of the result, not the
input.

If you specify an n such that a must be zero-padded or truncated, the
extra/removed values will be added/removed at high frequencies. One can
thus resample a series to m points via Fourier interpolation by:
a_resamp=irfft(rfft(a),m).

Notice how the last term in the input to the ordinary ifft is the
complex conjugate of the second term, and the output has zero imaginary
part everywhere. When calling irfft, the negative frequencies are not
specified, and the output array is purely real.